Let $\mu(x)dx$ be a mesure in $\mathbb{R}^{2n-2}$, where $\mu$ ( $C^\infty$ and positive function) be the density of the volume in the sense that $Vol_\mu(B_r)=\int_{B_r}\mu(x)dx$, where $B_r$ be the ball of raduce $r$ on $\mathbb{R}^{2n-2}$ . we suppose that $\mu(x)dx=d\Gamma$, By stockes we get$$Vol_\mu(B_r)=\int_{B_r}\mu(x)dx=\int_{B_r}d\Gamma=\int_{S_r}\Gamma$$ where$S_t$ be the sphere in $\mathbb{R}^{2n-3}$ the question is: can we explain the area of $S_r$ as a function of $\mu$?
Relationship between volume density and area density
dg.differential-geometrymeasure-theoryprobability-distributionsgeometric-measure-theoryspherical-varieties
SAMIR MAROUANI
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